Ophthalmic lens for the compensation of eyesight defects are well known. Multifocal ophthalmic lenses are a type of ophthalmic lens which in practice often comprise an aspherical face, and a face, which is spherical or toric, machined to match the lens to the wearer's prescription.
Progressive ophthalmic lenses usually comprise a far vision region, a near vision region, and a progressive corridor (or channel) there between. The progressive corridor provides a gradual power progression from the far vision zone to the near vision zone without a dividing line or a prismatic jump.
For multimodal lenses, the power in the various far, intermediate and near vision regions is determined by the prescription. A prescription may for example define lens characteristics such as a power value for near vision, a power value for far vision, an addition, and possibly an astigmatism value with its axis and prism.
Generally, the dispensing of a particular progressive addition lens to a wearer involves selecting a progressive addition lens design from a range of available progressive addition lens designs based on certain visual requirements of the wearer.
In a common method for producing progressive multifocal lenses according to optical lens parameters including prescription data, a semi-finished lens blank having suitable optical characteristics is selected based on a prescription. Typically the semi-finished progressive lens blank comprises a front progressive multifocal surface and a back spherical surface. The back surface of the semi-finished lens blank is then machined and polished to match the far-vision prescription.
An alternative method for producing multifocal progressive lenses uses less expensive single vision semi-finished lens blanks having a front spherical surface and a back spherical surface. Based on the optical lens parameters including prescription parameters and other wearer parameters, a single vision semi-finished lens blank having a suitable optical power is selected. A progressive surface design is then computed, for example obtained by optimisation, in accordance with optical lens parameters, and the back surface of the lens blank is machined and polished to produce the desired progressive surface. Although less expensive, this method for producing multifocal progressive lenses is relatively time consuming, partly due to the computational complexity of computing the progressive surface for each prescription.
The optimisation of an ophthalmic lens involves determining coefficients a of a surface equation S(α) for defining a surface layer of one of the surfaces of the lens according to optical lens parameters denoted as λ. A lens surface may be composed of one or more surface layers and thus defined by one or more surface equations. Optical lens parameters include wearing parameters λ including optical prescription data such as prescribed values defining surface characteristics including sphere, cylinder, axe, prism power, addition, progression length etc; personalisation parameters, environmental factors, positioning parameters etc; for the wearing of the optical lens. The surface equation coefficients a are determined such that a function Fλ(α) known as a merit function and which represents the optical defects of an optical lens, is kept to a minimum.
In some cases in addition to coefficient α a set of equality constraints CEλ(α)=0 and inequality constraints CIλ(α)≦0 should be respected. These constraints may include prescription constraints relating to the near vision NV and the far vision FV zone or to lens thickness constraints, and the like.
The optimisation of an optical lens may thus be mathematically represented by the following problem:
                    {                                                                              min                  α                                ⁢                                                      F                    λ                                    ⁡                                      (                    α                    )                                                                                                                                                                CE                    λ                                    ⁡                                      (                    α                    )                                                  =                0                                                                                                                              CI                    λ                                    ⁡                                      (                    α                    )                                                  ≤                0                                                                        (        1        )            
In many cases the function Fλ(α) is not continuous in variables λ. For example the base curves chart which is an allocation law of the curvature radius of one of the surfaces of the lens can introduce discontinuities to the function Fλ(α)
The set O of all optical lens parameters λ can be divided into M distinct and connected zones Oi (i=1 . . . M) of optical lens parameters in which the functions Fλ(α), CEλ(α) and CIλ(α) are continuous. The continuous functions associated with these zones are denoted as Fλi(α)(i=1, . . . M), CEλi(α)(i=1, . . . , M) and CIλi(α)(i=1, . . . , M).
This leads to the following representations:
                                          F            λ                    ⁡                      (            α            )                          =                  {                                                                                                                                        F                        λ                        1                                            ⁡                                              (                        α                        )                                                              ⁢                                                                                  ⁢                    if                    ⁢                                                                                  ⁢                    λ                                    ∈                                      O                    1                                                                                                                        …                  ⁢                                                                                                                                                                                                                                F                        λ                        M                                            ⁡                                              (                        α                        )                                                              ⁢                                                                                  ⁢                    if                    ⁢                                                                                  ⁢                    λ                                    ∈                                      O                    M                                                                                                          (        2        )                                                      CE            λ                    ⁡                      (            α            )                          =                  {                                                                                                                                        CE                        λ                        1                                            ⁡                                              (                        α                        )                                                              ⁢                                                                                  ⁢                    if                    ⁢                                                                                  ⁢                    λ                                    ∈                                      O                    1                                                                                                                        …                  ⁢                                                                                                                                                                                                                                CE                        λ                        M                                            ⁡                                              (                        α                        )                                                              ⁢                                                                                  ⁢                    if                    ⁢                                                                                  ⁢                    λ                                    ∈                                      O                    M                                                                                                          (        3        )                                                      CI            λ                    ⁡                      (            α            )                          =                  {                                                                                                                                        CI                        λ                        1                                            ⁡                                              (                        α                        )                                                              ⁢                                                                                  ⁢                    if                    ⁢                                                                                  ⁢                    λ                                    ∈                                      O                    1                                                                                                                        …                  ⁢                                                                                                                                                                                                        CI                      λ                      M                                        ⁢                                                                                  ⁢                                          (                      α                      )                                        ⁢                                                                                  ⁢                    if                    ⁢                                                                                  ⁢                    λ                                    ∈                                      O                    M                                                                                                          (        4        )            
If we make the assumption that the optimisation problem represented by formula (1) has a unique solution, then the solutions of the problem are continuous in each zone Oi(i=1, . . . , M).
When an order for a personalised optical lens defined by a set of optical lens parameters λ arrives in a prescription laboratory problem 1 is solved for each prescription using an adapted algorithm. Such a process is however time consuming and complex.